Conventionally, vane pumps have been known. For example, the Japanese Patent Application Public Disclosure No. 2004-92395 describes a vane pump in which a notch is provided at an initiating end of a discharge port. When the stroke shifts from a suction stroke to a discharge stroke, a pump chamber first communicates with the notch. In this vane pump, an increase in pressure in the pump chamber is realized by a working fluid which is introduced from a discharge port through the notch.